Detail from the cover of Stick Man by Julia Donaldson and Axel Scheffler

The 19th-century historian Thomas Babington Macaulay knew Paradise Lost by heart; I know Room on the Broom. Whether or not this says something about the decline of civilisation, it's certainly a tribute to the modern literary phenomenon that is Julia Donaldson and Axel Scheffler. Like countless parents all over the country, I've read their books – The Gruffalo, Monkey Puzzle, A Squash and a Squeeze and the others – so many times the words have taken on the quality of a mantra. The definition of "incantation" is a "ritual recitation of verbal charms or spells to produce a magic effect" and that just about sums it up. This has, I guess, always been the case with good books for young children, but Donaldson's light-on-their-feet fables, with their rhythms and repetitions, especially fit the bill, and encourage the eerie idea that at, say, 7.15pm on any given night, tens of thousands of glazed-eyed mums and dads are, in unison, chanting the immortal words: "My tie is a scarf for a cold giraffe". This is almost a religion.

Which is the best of the books? People have come to blows over less intractable questions. I have a particular fondness for The Smartest Giant in Town, partly because, with typical wit, Axel Scheffler quietly embeds references to nursery rhymes in the illustrations (a pig with a pile of bricks in a wheelbarrow, a black sheep with three bags of wool, and so on). And I very much like looking at, and learning about, the different types of fish in Tiddler. The newest book, Zog, impressively manages to dovetail the goings-on in a school for dragons with what amounts to a plug for Médecins Sans Frontières. Then again, I know one colleague on the Guardian books desk who is adamant that The Snail and the Whale is the ne plus ultra of the collaboration, and I admit the penguin diving off the iceberg gives me pleasure every time I get to that page.

But only one of these modern classics features Christmas, and that's Stick Man. As Susanna Rustin told us in her profile of Julia Donaldson, the idea for the book came from Scheffler, when, in The Gruffalo's Child, he drew the creature's intrepid daughter holding a stick doll. As Donaldson said, kids love sticks, and the idea of a living stick who has a house (the "family tree") and who might go for a jog is a natural next step. Mistaken for an ordinary stick, the jogging Stick Man is chased by a dog in a park and begins a series of rather fraught adventures. (My favourite bit of Scheffler-magic in this book is the drawing of the dog when he's told he has to be put on a lead – downturned mouth, ears flat, tail limp, he is disappointment comically embodied.) A girl throws Stick Man – thinking him a mere Pooh-stick – into a river; a swan weaves him into its nest; he floats out to sea, and is washed up on a beach where he adorns a sandcastle. The seasons change and winter sets in; Stick Man is lonely, lost and cold. With his family pining for him back in the family tree, it seems he is to be burned as firewood . . .

This is not the place to explore intricate psychological and socio-economic readings of the story – concepts of persecution, exploitation and identity (over and over, he pleads that he's not an inanimate bit of wood, but a living being – "I'm Stick Man, I'm Stick Man, I'M STICK MAN, that's me!"). Much more important for our purposes is the appearance near the end of Santa, who gets stuck in the chimney underneath which Stick Man languishes in the grate. Our hero grabs Santa's boot, tugs him down, receives his hearty thanks, and is soon sitting alongside him in his sleigh helping deliver toys "to fast-asleep girls and to fast-asleep boys", before being reunited with Stick Lady and his stick children three. From this moment on, he's "sticking right here in the family tree." It's a Christmas miracle.

Stick Man might not – I think this is fair – be the very best of Donaldson and Scheffler's work, but even their average is much, much better than most, and it'll no doubt make up a good portion of my seasonal reading. I've notched up a dozen or so well-received recitals already this winter, and I'd say I had, at a rough estimate, about 112 more to go. If you're travelling this Christmas, don't forget to pack your copy. "Stick Man, oh Stick Man, beware of the snow!"